The market demand for a particular good in city A is given by Q(A) = 32...

The market demand for a particular good in city A is given by Q(A) = 32 ? 0.5P (for P ? 64). This market is served by a single firm (monopoly) whose marginal cost of production is 4 dollars per unit (so total cost of producing Q units is 4Q).

(a) Find the equation for the firm’s marginal revenue function. Draw the demand, marginal cost and marginal revenue curves on one graph.

(b) What are the profit-maximizing price and quantity for the monopolist?

(d) What is consumer surplus in this market? How large is the deadweight loss resulting from monopoly pricing?

Solutions

Expert Solution

Market demand function is Q = 32 – 0.5P or inverse demand function is 0.5P = 32 – Q or P = 64 – 2Q

a) Now we have P = 64 – 2Q. Total revenue function is TR = 64Q – 2Q^2. Marginal revenue is the derivative of TR so MR = 64 – 4Q

b) Monopolist equates MR = MC

64 – 4Q = 4

Q = 60/4 = 15 units and so monopolist charges a price of 64 – 2*15 = $34 per unit.

c) Profit = TR – TC = 15*34 – 4*15 = 15*30 = $450. Mark up = (P – MC)/P = (34 – 4)/34 = 0.88

d) CS = 0.5*(Max price – current price)*current qty = 0.5*(64 – 34)*15 = $225

DWL = 0.5*(34 – 4)*(30 – 15) = $225

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

The market demand for a particular good in city A is given by QA = 32...

The market demand for a particular good in city A is given by QA = 32 − 0.5PA (for PA ≤ 64). This market is served by a single firm (monopoly) whose marginal cost of production is 4 dollars per unit (so total cost of producing Q units is 4Q). (a) Find the equation for the firm’s marginal revenue function. Graph the demand, marginal cost, and marginal revenue curves on one graph. (b) What are the profit-maximizing price and quantity...

The market supply is given by P = 20 + Q. The market demand for good...

The market supply is given by P = 20 + Q. The market demand for good X is given by P = 100 - 2Q - PZ. PZ is the price of a related good Z. Find the market equilibrium for good X when PZ equals 38; denote the equilibrium as P1 and Q1. Find the market equilibrium for good X when PZ equals 44; denote the equilibrium as P2 and Q2. Using the midpoint method, the price elasticity of...

The inverse market demand for a homogeneous good is given by p = 1 – Q,...

The inverse market demand for a homogeneous good is given by p = 1 – Q, where p denotes the price and Q denotes the total quantity of the good. The good is supplied by three quantity-setting firms (Firm 1, Firm 2, and Firm 3) competing à la Cournot, each producing at a constant marginal cost equal to c > 0. a) Derive the best reply of Firm 1. b) Compute the Cournot-Nash equilibrium quantity and profits of Firm 1....

The market demand function for a good is given by Q = D(p) = 800 −...

The market demand function for a good is given by Q = D(p) = 800 − 50p. For each firm that produces the good the total cost function is TC(Q) = 4Q+( Q2/2) . Recall that this means that the marginal cost is MC(Q) = 4 + Q. Assume that firms are price takers. In the short run (with 100 firms), and assume that the government imposes a tax of $3 per unit. (a) What would be the new equilibrium...

The inverse demand function in a market is given by p=32-Q where Q is the aggregate quantity produced.

The inverse demand function in a market is given by p=32-Q where Q is the aggregate quantity produced. The market has 3 identical firms with marginal and average costs of 8. These firms engage in Cournot competition. a) How much output does each firm produce? b) What is the equilibrium price in the market? c) How much profit does each firm make? d) Consider a merger between two firms. Assuming that due to efficiency gains from the merger,...

Suppose a country is large in the market for a particular good. There, the demand is...

Suppose a country is large in the market for a particular good. There, the demand is D = 9000 - 30P and the supply is S = -1000 + 10P. Moreover, when there is trade, this country is an importer, the import demand being MD = 10000 - 40P and the export supply being XS = -3000 + 60P. 1) In the absence of tariff, what is the total welfare in this country when there is trade? 2) What is...

Consider a market for a good characterized by an inverse market demand P(Q) = 200−Q. There...

Consider a market for a good characterized by an inverse market demand P(Q) = 200−Q. There are two firms, firm 1 and firm 2, which produce a homogeneous output with a cost function C(q) =q2+ 2q+ 10. 1. What are the profits that each firm makes in this market? 2. Suppose an advertising consultant approaches firm 1 and offers to increase consumers’ value for the good by $10. He offers this in exchange for payment of $200. Should the firm...

uppose that demand is given by qa = 32 – pa in Market A and by...

uppose that demand is given by qa = 32 – pa in Market A and by qb = 40 – pb in Market B where pi, and qi are price and output in market i = a, b, respectively. Marginal cost is constant and equal to 4. Fixed costs are zero. b) . Find the profit maximizing prices, quantities and profit if the monopolist can price discriminate. c) . Find the profit-maximizing price, quantity and profit if the monopolist cannot...

The demand function for a good is given as Q = 130-10P.

The demand function for a good is given as Q = 130-10P. Fixed costs associated with producing that good are €60 and each unit produced costs an extra €4. i). Obtain an expression for total revenue and total costs in terms of Q ii). For what values of Q does the firm break even iii). Obtain an expression for profit in terms of Q and sketch its graph iv). Use the graph to confirm your answer to (ii) and to...

In the perfectly competitive market for skateboards in a particular city, market supply is given by...

In the perfectly competitive market for skateboards in a particular city, market supply is given by the following equation: P=30+3Q and market demand is given by the following equation: P=250-Q where P is the price per skateboard and Q is the number of skateboards. To raise revenue, the city decides to impose a $10 tax on each skateboard sold. What share of the total tax burden will be borne by consumers? What share of the total tax burden will be...

Subjects